Question

The graph models function R. The table of values models function S. Which statement is true about these functions?

Answer 1

Answer: OPTION D.

Step-by-step explanation:

The rate of change of a linear function is also known as "Slope".

The slope can be calculated with the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Choose two points on the function "R" graphed:

$(1,0)\\(0,-3)$

You can say that:

 $y_2=-3\\y_1=0\\\\x_2=0\\x_1=1$

Substituting values into the formula, you get:

$m=\frac{-3-0}{0-1}=3$

Choose two point from the table that models the function "S":

$(4,21)\\(6,31)$

You can say that:

 $y_2=31\\y_1=21\\\\x_2=6\\x_1=4$

Substituting values into the formula, you get:

$m=\frac{31-21}{6-4}=5$

Therefore, you can conclude that the function "S" has a greater rate of change than Function "R".

Answer 2

Answer:

D: Function S has a greater rate of change than Function R.

Step-by-step explanation:

Function S has a greater rate of change than Function R.

Function R → m =

rise

run

=

6

2

= 3. Function S → m =

change in y

change in x

=

31 − 21

6 − 4

=

10

2

= 5

Since 5 > 3, function S has a greater rate of change.